Optical length measurements, made by interferometry, are highly sensitive and adaptable to the study of a wide range of physical phenomena because they sensitively measure small induced changes in the optical length of a material medium, of the order of a fraction of an optical wavelength.
A number of physical and chemical phenomena may account for a spatial variation in the optical length of a condensed phase material, which may be interferometrically probed under appropriate conditions. Two and three dimensional variations in the surface topography of a material result in thickness (and therefore optical length) variations on the order of one or more optical wavelengths, which may be spatially imaged by interferometry. Two and three dimensional variations in the chemical composition or physical micro-structure of a material may produce both spatially distributed thickness variations and spatial variations in the index of refraction. All of these effects may be probed under suitable conditions, and, potentially, imaged in two dimensions by interferometry.
In addition to the static or intrinsically occurring spatial variations in the optical length of a material, additional optical length variations may be induced in a material in the presence of externally applied perturbations. A number of physical and chemical phenomena provide mechanisms for inducing spatially distributed changes in the optical length of a condensed phase material, which may then be interferometrically probed. Such mechanisms could include thermal or electromagnetic excitation, or acoustic or mechanical perturbation of the material. When interferometry is used to record images of the optical length changes induced in a material by such applied external perturbations, it may provide a method of imaging the thermal, acoustic, optical or topographic properties of the material, depending on the nature of the externally applied perturbation.
Because of the many physical and chemical phenomena which are capable of producing optical length changes in a material, which interferometry may potentially probe with very high optical length resolution, imaging methods based on interferometry have widespread applications in industrial measurement. Some examples include interferometric imaging of materials or structures excited using thermal energy, ultrasonic waves, or mechanical vibrations.
When a material sample is subjected to a perturbation such as one of the above-mentioned perturbations, any resulting changes in the material optical length may be potentially sensed by an interferometer. Optical length variations occurring along the transverse coordinates of the interferometer may be probed to form an interferometric image: the transverse coordinates of the interferometer, which are also the image coordinates of the phase image, are defined as occupying orthogonal directions, namely (x,y), which lie in the plane perpendicular to the probe beam axis of optical propagation (the "z" axis), which will be defined hereinafter. The primary interferometric image produced by the interferometer is called a spatial interferogram. The spatial interferogram is defined as an image formed by the superposition of the probe and reference beams in the exit pupil plane of the interferometer or in a plane conjugate to the exit pupil plane, with the aperture stop of the interferometer assumed to be located at the test medium. The spatial interferogram is recorded by a camera, which is considered to be a generalized imaging device composed of an array of optical sensing elements (or image pixels) operating over the wavelength range used by the interferometer beams, and the information is stored in a a data storing and processing system, e.g. a computer.
Known interferometric phase imaging apparatuses generally consist of a phase imaging interferometer and an external imaging system, the latter briefly described above. The interferometer stage consists of the following elements:
a) a radiation source normally containing a band of wavelengths lying in the ultraviolet to the far infrared (shorter wavelengths such as x-rays or longer wavelengths such as those pertaining to microwave and radio-frequency fields are not excluded in principle); the radiation source emits a source beam having a spatial coherence length of 10-100 cycles or greater of the radiation at all wavelengths; PA1 b) an input plane or surface at which the source beam is separated (by partial reflection or other means) into one (or more) probe beam which propagates along a path called the probe arm of the interferometer, and one (or more) reference beam which is phase coherent with the probe beam and which propagates along a path called the reference arm of the interferometer; PA1 c) a material medium, on which property measurement is accomplished by means of the interferometry apparatus; the material medium is also called the test medium, and is intersected by the probe beam which experiences a one, two or three dimensional spatial variation in optical phase shift with respect to the coordinates (x,y) and z; and PA1 d) an output plane or surface in which the probe and reference beams are superimposed so as to produce electromagnetic wave interference, thus forming an output beam. PA1 a radiation source providing a source beam along an axis of propagation; PA1 a polarizer for plane polarizing said source beam along a single polarizing axis lying in a plane perpendicular to said axis of propagation, thereby producing a plane polarized beam; PA1 a first beam splitter for separating said polarized source beam into plane polarized probe and reference beams with the test medium intersecting said probe beam, having electromagnetic influence thereon; PA1 a second beam splitter at which said probe beam and said reference beam are interferentially combined into an output beam, whereas one of either said probe beam or said reference beam, called the plane polarized component of said output beam, is polarized in a plane perpendicular to said beam axis of propagation, said plane polarized output component having an electric field vectorially composed of a first and a second electric field polar components of equal magnitude aligned orthogonal to each other along respective first and second polar axes, and where, at said second beam splitter, the other one of said probe and said reference beam, being not the plane polarized output component, called the elliptically polarized component of said output beam, has polarization being either one of circular or elliptical, in which said elliptical polarization has associated major and minor axes, and where said major and minor axes of said elliptically polarized output component align colinearly with said polar axes of said plane polarized output component, and where, at said second beam splitter, the electric field components of said probe and said reference beam which are aligned along said first polar axis interfere with each other, but distinctly of the electric field components of said probe and said reference beam which are aligned along said second polar axis; PA1 a wave plate assembly intersecting either one of said probe or said reference beam, where so selected beam is giving rise to said elliptically polarized output component, said wave plate assembly being aligned to confer on said beam at all positions downstream of said wave plate assembly and upstream of and at said second beam splitter, either one of a state of circular polarization or of elliptical polarization, where said elliptical polarization occurs with unequal maximum electric field magnitudes projecting along major and minor axes which align along said polar axes of said plane polarized output component at said second beam splitter, thereby imposing a phase difference of N*.pi./2 radians where N is any signed odd integer, between the electric field component of said elliptically polarized output component at said second beam splitter aligned along said first polar axis and the electric field component of said elliptically polarized output component aligned along said second polar axis; PA1 a single polarizing beam splitter accomplishing polarized segregation of said output beam according to alignment of electric field components of said probe and reference beams along said first and said second polar axes so as to obtain a first interferogram comprising the components of said output beam aligned along said first polar axis and a second interferogram comprising the components of said output beam aligned along said second polar axis; and PA1 image recovering means, for recovering images of said first and second interferograms. PA1 a radiation source providing a source beam along an axis of propagation; PA1 a polarizer for plane polarizing said source beam along a single polarizing axis lying in a plane perpendicular to said axis of propagation; PA1 a first beam splitter for separating said plane polarized source beam into plane polarized probe and reference beams with the test medium intersecting said probe beam, having electromagnetic influence thereon; PA1 at least one reflective element intersecting at least either one of said probe and said reference beam, whereby said probe beam and said reference beam are redirected to said first beam splitter and are interferentially combined thereat into an output beam, whereas one of either said probe beam or said reference beam redirected to said first beam splitter, called the plane polarized component of said output beam, is plane polarized in a plane perpendicular to said beam axis of propagation, said plane polarized output component having an electric field vectorially composed of a first and a second electric field polar components of equal magnitude aligned orthogonal to each other along respective first and second polar axes, and where, at said first beam splitter, the other one of said probe and said reference beam redirected thereto, being not the plane polarized output component, is called the elliptically polarized component of said output beam, having polarization being either one of circular or elliptical, where said elliptical polarization has associated major and minor axes with unequal maximum electric field magnitudes projecting along said axes, and where said major and minor axes of said elliptical polarization align colinearly with said polar axes of said plane polarized output component, and where, at said first beam splitter, the electric field components of said redirected probe and reference beams aligned along said first polar axis interfere with each other, but distinctly of the electric field components of said redirected probe and reference beam which are along said second polar axis; PA1 a wave plate assembly intersecting either one of said probe or said reference beam, where so selected beam is not the beam giving rise to said plane polarized output component, said wave plate assembly being aligned to confer on said beam at all positions downstream of said wave plate and upstream of and at said first beam splitter, either one of a state of circular polarization or of elliptical polarization, where said elliptical polarization occurs with unequal maximum electric field magnitudes projecting along major and minor axes which align along said polar axes of said plane polarized output component at said first beam splitter, thereby imposing a phase difference of N*.pi./2 radians where N is any signed odd integer, between the electric field component of said elliptically polarized output component along said first polar axis and the electric field component of said elliptically polarized output component along said second polar axis; PA1 a single polarizing beam splitter accomplishing polarized segregation of said output beam according to alignment of electric field components of said redirected probe and reference beams along said first and said second polar axes so as to obtain a first interferogram comprising the components of said output beam aligned along said first polar axis and a second interferogram comprising the components of said output beam aligned along said second polar axis; and PA1 image recovering means, for recovering images of said first and second interferograms. PA1 a) providing a source beam polarized along an axis lying in a plane perpendicular to said beam axis of propagation; PA1 b) splitting the beam with said first beam splitter into two distinct probe and reference beams which are substantially identical at said first beam splitter; PA1 c) merging, at said second beam splitter said probe beam and said reference beam into at least one output beam, and maintaining, in either one of said probe or said reference beam, a state of plane polarization at said second beam splitter, in which the electric field components of said plane polarized beam at said second beam splitter are vectorially composed of a first and second polar components of equal magnitude oriented orthogonally to each other along first and second polar axes in a plane perpendicular to said probe beam axis of propagation; PA1 d) intersecting said probe beam with the test medium and intersecting with the wave plate element a selected beam among either one of said probe or said reference beam, being not said plane polarized output beam at said second beam splitter, whereby said wave plate element confers either one of a state of circular or elliptical polarization to said selected beam at said second beam splitter, and where the major and minor axes of said elliptical polarization are aligned colinearly with said polar axes of said plane polarized output beam at said second beam splitter, thereby producing a phase difference of N*.pi./2 where N is any odd signed integer, between the electric field components of said probe and reference beams aligned along said first polar axis and the electric field components of said probe and reference beams aligned along said second polar axis at said second beam splitter; PA1 e) producing at said second beam splitter interference between the components of said probe and reference beam aligned along said first polar axis and a distinct interference between the components of said probe and reference beam aligned along said second polar axis; PA1 f) segregating said output beam according to its polarization with the polarizing beam splitter wherein the first and second polar components of said output beam will be separated so as to allow distinct interferograms to be formed, whereby a quadrature interferogram will be formed from said first polar components and an in-phase interferogram will be formed from said second polar components; and PA1 g) recovering the images of the quadrature and in-phase interferograms with the image recovering means.
Other external components with which the interferometer is equipped include: a set of image transfer elements such as lenses, mirrors or other beam directing elements, operating over the wavelength range of the interferometer, where the set of image transfer elements transfer an image of the wave interference occurring in the interferometer exit pupil plane to the imaging device or camera consisting of an array of radiation intensity sensing elements. If negligible diffraction or refraction occurs between the test medium and the output plane (as is usually the case), an image of the interference at the output plane provides a good approximation to the image observed in the exit pupil plane and the imaging system may have as its object plane the output plane of the interferometer (or points in the neighborhood thereof).
It will be assumed that the probe and reference beams have spatial coherence over a length of at least 10 cycles at each wavelength in the interferometer's wavelength range. Within the beam spatial coherence length, said beam propagates with wavefronts of deterministic phase dependence, which obey the laws of coherent scalar wave propagation theory.
In practice, through the use of lasers as the radiation source, which is common in interferometry, a coherence length on the order of centimeters to meters is readily obtainable. Hence the probe and reference beams often behave as though they were completely spatially coherent over distances which are large relative to the probe and reference beam path lengths in the interferometer, when laser sources are used. This is the usual condition assumed for the description of probe and reference beam propagation in the present specification.
In many cases, both the probe and reference beams propagating in the interferometer will have nearly flat phase fronts, and will propagate approximately as plane waves. This means that the divergence or convergence of the beams in the interferometer will be small in these cases. Such a beam has a well defined axis of propagation which is seen to be oriented in the direction colinear to the surface normal of the beam front at the central axis of the beam. The central axis of such a beam will spatially coincide with the centroid of the optical intensity distribution, as averaged in a direction along the beam's wavefront or wavefronts. These transverse orthogonal coordinate directions are assigned the notations x and y. It is normally desirable for the probe and reference beams, when superimposed at the output plane, to have nearly flat wave fronts, where any transverse length displacements of the probe wave front arising from phase shifts imparted by the test medium are of the order of the probe beam wavelengths.
In the generalized phase imaging interferometer it is normally desirable that probe and reference beams have phase fronts which are flat or slowly varying along the x and y directions. This flatness is a desirable property for the probe and reference beams forming an interferogram at the output plane or surface. If the probe and reference beams have large intrinsic phase front curvatures at the output surface, the spatial interferogram may become highly sensitive to small displacements in the transverse coordinates of central axis positions of the superimposed probe and reference beams. Hence the output surface is usually chosen to be planar to a good approximation, and in the discussion hereinafter, the term output plane, is used in preference to output surface. It is also usually desirable for the source beam arriving at the input plane to be flat. If the radiation produced by a given source is not collimated, a set of optional beam collimating components may be located in the source beam path between the radiation source and the input plane of the interferometer, to insure adequate phase front flatness of the probe and reference beams propagating in the interferometer.
As known to the person skilled in the art, the purpose of an imaging interferometer is to measure optical length variations in the test medium, which may be obtained by mathematically processing the experimental results retrieved by the imaging system. The experimental result that must be obtained is the phase variation in the probe beam .DELTA..phi.(x,y), which may be determined through the interferograms formed with the probe and reference beams.
The test medium optical length variation may be intrinsic to the medium, or may be induced as the result of a perturbation mechanism. There are three possible means by which the interferometer may probe the phase distribution in the test medium (TM): (i) by propagation of the probe beam through the test medium with full (greater than 99%) or partial optical transmission of the probe beam by the medium; (ii) by full (greater than 99%) or partial reflection of the probe beam at a surface of the test medium;(iii) some combination of full or partial reflection at a surface of the TM with full or partial transmission by the constituent medium or media comprising said TM. In the case where the test medium is composed of an inhomogeneous assembly of contiguous layers of media, reflection may occur at one or possibly more of the interfaces contained in such an assembly.
The relationship between the radiation phase shift measured by an interferometer and the measured spatial interferogram must next be examined. The equations given hereinafter pertain to a generalized phase imaging interferometer equipped with a highly spatially coherent source such as that supplied by a laser.
Assuming that the probe and reference beams are highly collimated in a generalized phase imaging interferometer, under the above conditions, a cosine or "corrected in-phase" interferogram may be obtained through equation (1), ##EQU1## in which: .DELTA..phi..sub.c (x, y) is the interferometric phase difference between the interferometer probe and reference beams, since the probe and reference beams originate from a same source beam and assuming nearly flat phase fronts with the condition of good matching of the probe and reference beam central axes;
I(x,y) is the output beam intensity (the "in-phase" interferogram), as measured on the interferogram by means of the imaging system, as an array of pixels having individual intensities and each having corresponding respective transverse coordinates (x,y); PA0 I.sub.r (x,y) is the reference beam intensity, as measured independently while the probe beam is optically sealed with a suitable shutter; and PA0 I.sub.p (x,y) is the probe beam intensity, as measured independently while the reference beam is optically sealed with a suitable shutter.
Thus, the first step in any phase reconstruction method is a linear recording of the intensity interferograms I(x,y), I.sub.r (x,y) and I.sub.p (x,y) by an imaging device, in which the output beam intensity distribution incident on the sensing elements of the camera is sampled as a two dimensional array of picture elements or pixels, where the camera signal generated at an individual pixel is linearly proportional to the integral light intensity over that pixel's area. The recovery of .DELTA..phi..sub.c (x,y) from interferograms measured by the interferometer is termed "phase reconstruction". Once the images of the probe beam intensity, of the reference beam intensity and of the interfering beams intensity are captured, they are mathematically processed through equation (1), for recovering the optical phase difference over the interval from 0 to .pi. radians. The inverse cosine function cannot recover negative values of the phase argument, however, and two quadrants of angular correction, from .pi. to 2.pi., cannot be accurately reconstructed from the cosine interferogram alone. Note that in the absence of mutual interference, the probe and reference beam intensity images are highly stable over relatively long periods of time, and need not be recorded in rapid succession with the interferogram.
For phase reconstruction over the full angular interval from 0 to 2.pi. radians, a quadrature component of the cosine interferogram, namely + or -sin(.DELTA..phi..sub.c (x,y)), must be recovered in addition to the cosine interferogram. Such a quadrature component would have a value of the optical phase which is a constant ninety degrees greater or less, at all transverse spatial (x,y) positions, than.DELTA..phi..sub.c (x,y), the intrinsic interferometric phase.
The quadrature component of the corrected spatial interferogram may be recovered experimentally by measuring a so-called quadrature interferogram. The quadrature interferogram can be recovered by physically imposing a precise positive or negative 90 degree optical phase offset between the probe and reference beams at all (x,y) coordinate positions, over and above the intrinsic interferometric phase, .DELTA..phi..sub.c (x,y), existing between probe and reference beams. This imposed differential phase offset must be applied precisely, without any significant error, over all of the interferometric transverse coordinates. The positive quadrature interferogram is given the notation I.sub.q (x,y), and yields a sine interferogram expression as in equation (2). ##EQU2##
It is also experimentally possible to generate a so called negative quadrature interferogram, which is mathematically expressed similarly to equation (2), but then the negative sine interferogram (-sin(.DELTA..phi..sub.c)) will be recovered. The negative quadrature interferogram is recovered by physically adding a precise -.pi./2 radians phase value to the interferometric phase, .DELTA..phi..sub.c (x,y), between the probe and reference beams, where the probe beam lags the reference beam by .pi./2 radians, at all transverse spatial positions in the interferogram.
A recovery of .DELTA..phi..sub.c (x,y) may be made with good accuracy from the corrected interferogram data by computing: ##EQU3## when .vertline.sin(.DELTA..phi..sub.c).vertline..ltoreq.cos .vertline.(.DELTA..phi..sub.c).vertline.and: ##EQU4## when .vertline.cos(.DELTA..phi..sub.c).vertline..ltoreq..vertline.sin(.DELTA..p hi..sub.c).vertline..
Phase reconstructions may thus be made over all four Cartesian quadrants by consideration of the signs of the corresponding pairs of sine and cosine terms in equations (3) and (4).
If one measures the negative quadrature interferogram instead of the positive quadrature interferogram, the equations (1) to the cosine interferogram and (2) as modified to the negative sine interferogram (-sin(.DELTA..phi..sub.c)), will then reconstruct the negative of the interferometric phase. Hence, a recording of either the positive or negative quadrature interferogram will enable recovery of the interferometric phase image. The term quadrature interferogram thus refers equally to either a positive quadrature or negative quadrature interferogram.
In advanced applications of interferometric imaging, an externally applied perturbation (such as heating, acoustic perturbation, etc.) causes a change in the transverse optical length distribution of the test medium. If any significant deviations from uniformity of the optical phase fronts are contributed by imperfections in the optical components placed in the probe or reference beam, a background phase image contribution will be produced which is additive with the phase image from the test medium. Together, these background image contributions sum to produce a phase image, .DELTA..phi..sub.c (x,y).sub.unperturbed. is desired, in such a case, to measure images of the applied perturbation independently of any intrinsic optical length variations existing in the material in the absence of said applied perturbation.
To accomplish this, a first phase image .DELTA..phi..sub.c (x,y).sub.unperturbed is computed as described above and expressed in equations (3) and (4) from the interferometric image without any external perturbation, and is then subtracted from a second phase image .DELTA..phi..sub.c (x,y).sub.perturbed computed from equations (3) and (4) while the test medium is being subjected to an external perturbation.
Many established interferometric imaging methods require the recovery of the phase image of an externally perturbed test medium for a complete physical interpretation of the image formation process in a material, obtained through the differential measurement explained hereinabove.
Any method which reconstructs the interferometric phase image, especially when such a method is applied for the purposes of differential image subtraction as when external perturbation on the test medium is present, must be stable, accurate and rapid. Speed of measurement is especially desirable for two reasons. First, the perturbation applied to the test medium may be transient and the requirement for obtaining information at high speed may be essential. If the perturbation consists of an ultrasonic pulse applied to the sample, a measurement time of microseconds or less may be appropriate, for example. Second, the interferometer has high sensitivity to small optical and/or geometric displacements. In the differential measurement described hereinabove, the measurement of the phase images .DELTA..phi..sub.c (x,y).sub.perturbed and .DELTA..phi..sub.c (x,y).sub.unperturbed occur under conditions of precisely matched optical alignment. If the interferometer optical paths drift or displace between these image recordings, the differential measurement will be invalidated. Consequently, the shorter the interval of measurement between .DELTA..phi..sub.c (x,y).sub.perturbed and .DELTA..phi..sub.c (x,y).sub.unperturbed required by a given method, the higher the fidelity of the differential phase reconstruction made by that method.
The consideration of stability of the methods used to reconstruct .DELTA..phi..sub.c (x,y).sub.perturbed and .DELTA..phi..sub.c (x,y).sub.unperturbed in a differential subtraction scheme is also of paramount importance. Stability in this context is the degree to which the alignment geometry of the interferometer is preserved during the measurements of all spatial interferograms, and more particularly during the measurements of in-phase and quadrature interferograms. A resettable phase reconstruction method is one in which the optical alignment of the interferometer which produced the in-phase interferogram may be precisely restored after the quadrature interferogram is recorded. Finally, an accurate phase reconstruction measurement is one in which the measured quadrature interferogram has a highly uniform optical phase offset from the in-phase interferogram over all points of the image field, (x,y), where said phase offset absolute value is very close to .pi./2 radians (or some odd integral multiple thereof)
The key problem associated with a practical implementation of all interferometric phase measurement schemes is the requirement for a rapid, stable, accurate and resettable measurement of the quadrature (or conjugate quadrature) interferogram. The measurement of the quadrature interferogram, when performed correctly, requires a precise and accurate insertion of a .pi./2 radian optical phase offset between the probe and reference beams, over and above the inherent interferometric phase difference, .DELTA..phi..sub.c (x,y). If the interferometer is supplied by a helium/neon laser, for example, this entails a physical path length displacement (in air) of +632/4 nm, as applied to either the probe arm or reference arm of the interferometer. Furthermore, this phase offset must be applied uniformly at all transverse coordinates, (x,y), as the optical path length is varied, for example, using a micropositioning apparatus.
A classical method of imposing such a phase difference between the interferometer arms is to supply a precise translation of a reflecting surface, such as that of a mirror, to increase or decrease the probe or reference arm's length, as appropriate. The translation of either the probe or reference mirror requires a precise motion to be applied, where such motion is colinear with the optical axis of the reference or probe arm of the interferometer, depending on the arm chosen to which the translation is applied. As a mirror element is displaced, all points of its surface must move with a fixed alignment precisely normal to the axis of motion. Any displacement transverse to the axis of motion introduces an error into the spatially uniform .pi./2 radian offset required by the quadrature interferogram, relative to the in-phase interferogram. Hence, expensive precision translation equipment must be used to apply the optical path length difference to the instrument. The optical path length must be set and reset to the values assumed by the in-phase and quadrature measurements, and this operation must be applied without slippage or decentration of the motion control apparatus. Thus,the likelihood of non-negligeable experimental errors under these conditions is high.
A standard alternative to purely mechanical motion controllers is to use a piezoelectric element in which an applied electric field across the element effects a change in the element thickness. In such a case, it is likely that there will be a difficulty in accurately calibrating the element absolute thickness change in terms of the voltage applied to the element.
Finally, another difficulty of the above methods is that there will be a time lag between the measurement of the in-phase and quadrature interferograms, which will be in the order of a few tens to a few hundreds of milliseconds for a mechanical motion controller. In this time interval the interferometer may accidentally drift or becomed mis-aligned slightly. A time lag problem remains even if a piezoelectric element is used to effect the optical path length translation.
A better method of measuring .DELTA..phi..sub.c (x,y) which involves the introduction of no moving components into the interferometer, is by introduction into the reference or probe arm, of an electro-optic element which is optically transparent at the interferometer beam's wavelength. To vary the optical length of the arm into which the electro-optical element is inserted, a voltage is applied across the element, which varies the refractive index of the crystal, by an amount governed by the electro-optic coefficient of the crystal. Application of a sufficiently large potential difference across the element varies the refractive index of the crystal sufficiently to produce a .pi./2 phase shift in the reference arm of the interferometer. The beam propagating through the electro-optic element must be polarized along one of the principal axes of the electro-optic crystal in order to effect this phase shift, however. With this method, the electric field applied across the crystal must be stable and spatially uniform across the transverse dimensions of the reference beam. The crystal must be of a high optical purity to ensure that the electro-optical coefficient is spatially uniform for a given applied potential, across the transverse coordinates through which the beam propagates. Temperature variations might also have to be compensated depending upon the choice of electro-optical material. As with methods which use translation of the optical path, there will necessarily be a time lag between the measurement of the in-phase interferogram and the quadrature interferogram.
A phase imaging interferometer was reported in 1984 by the "Smythe and Moore" prior art reference [R. Smythe and R. Moore, "Instantaneous Phase Measuring Interferometry", Optical Engineering, 23(4), pp. 361-364 (1984)], which generates polarization isolated probe and reference beams with orthogonally aligned plane polarizations, which propagate along a pair of short physically separated paths, and are then recombined at partially reflecting surface, without mutual interference. Separate beams are then directed through separate polarizing beam splitters, for obtaining in-phase and quadrature interferograms. A more complete description of the Smythe & Moore reference apparatus will be given later, in the present specification.
For now, let us say that the Smythe/Moore interferometer apparatus forms the in-phase and quadrature interferograms in distinct spatial locations, and thus any transverse alignment difference between the in-phase and quadrature beam paths will effectively yield an error in the output data concerning the phase reconstruction. Also, the Smythe/Moore interferometer apparatus requires a minimum of four and as many as five wave plates for it to become operational; and a minimum of two and as many as three polarizing beam splitters. Thus, it is rather expensive to produce, and complex to assemble (up to five polarization axes adjustments).